Relationship: They have a relationship, they are in a relationship, is relationship always sexual in these contexts? Can it be pure friendship or a platonic one? In describing a boyfriend-girlfriend situation, when relationship is used, can it be anything other than sexual?
Together: Before he moved away, we had had 5 happy years together. Does together here imply living together? Can it be just boyfriend-girlfriend living apart, having enjoyed friendship for 5 years?